On a certain run of a commuter train, the average number of passengers is 532. A

Question

On a certain run of a commuter train, the average number of passengers is 532. And use standard deviation is 28. Assume the variable X representing the number of passengers is normally distributed. Find the probability that the number of passengers on this train will be a. Between 532 and 580 passengers. b. Less than 500 passengers. c. More than 475 passengers. The average salary for a group of graduates is $50,000, and the salaries are normally distributed with a standard deviation of $6000. Find the following probabilities a. An individual graduate will have a salary of at least $47,000. b. If there is a group of 12 graduates, find the probability their average salary will be at least $47,000.

Explanation / Answer

6.3)

a)

P(532 < X < 580) = P(X<580) - P(X < 532)

= P(Z < 580-532/28) - P(X < 532-532/28)

= P(Z < 1.7143) - P(Z < 0)

= 0.9568 - 0.5

= 0.4568

b)

P(X < 500) = P(Z < 500 - 532/28)

= P(Z < -1.1429)

=0.1265

c)

P(X > 475) = P(Z > 475 - 532/28)

= P(Z > -2.0357)

= 0.9791

6.4)

a)

P(X > 47000) = P(Z > 47000 -50000/6000)

= P(Z > -0.5)

= 0.6915

b)

P(X > 47000) = P(Z > 47000 -50000/6000/sqrt(12))

= P(Z > -1.7321)

= 0.9584

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